Abstract-This paper addresses the problem of learning optimal policies for satisfying signal temporal logic (STL) specifications by agents with unknown stochastic dynamics. The system is modeled as a Markov decision process, in which the states represent partitions of a continuous space and the transition probabilities are unknown. We formulate two synthesis problems where the desired STL specification is enforced by maximizing the probability of satisfaction, and the expected robustness degree, that is, a measure quantifying the quality of satisfaction. We discuss that Q-learning is not directly applicable to these problems because, based on the quantitative semantics of STL, the probability of satisfaction and expected robustness degree are not in the standard objective form of Qlearning. To resolve this issue, we propose an approximation of STL synthesis problems that can be solved via Q-learning, and we derive some performance bounds for the policies obtained by the approximate approach. The performance of the proposed method is demonstrated via simulations.

Our goal is to develop models that allow a robot to efficiently understand or "ground" natural language instructions in the context of its world representation. Contemporary approaches estimate correspondences between language instructions and possible groundings such as objects, regions, and goals for actions that the robot should execute. However, these approaches typically reason in relatively small domains and do not model abstract spatial concepts such as as "rows, " "columns, " or "groups" of objects and, hence, are unable to interpret an instruction such as "pick up the middle block in the row of five blocks. " In this paper, we introduce two new models for efficient natural language understanding of robot instructions. The first model, which we call the adaptive distributed correspondence graph (ADCG), is a probabilistic model for interpreting abstract concepts that require hierarchical reasoning over constituent concrete entities as well as notions of cardinality and ordinality. Abstract grounding variables form a Markov boundary over concrete groundings, effectively de-correlating them from the remaining variables in the graph. This structure reduces the complexity of model training and inference. Inference in the model is posed as an approximate search procedure that orders factor computation such that the estimated probable concrete groundings focus the search for abstract concepts towards likely hypothesis, pruning away improbable portions of the exponentially large space of abstractions. Further, we address the issue of scalability to complex domains and introduce a hierarchical extension to a second model termed the hierarchical adaptive distributed correspondence graph (HADCG). The model utilizes the abstractions in the ADCG but infers a coarse symbolic structure from the utterance and the environment model and then performs fine-grained inference over the reduced graphical model, further improving the efficiency of inference. Empirical evaluation demonstrates accurate grounding of abstract concepts embedded in complex natural language instructions commanding a robotic torso and a mobile robot. Further, the proposed approximate inference method allows significant efficiency gains compared with the baseline, with minimal trade-off in accuracy.

Abstract-This paper introduces time window temporal logic (TWTL), a rich expressivity language for describing various time bounded specifications. In particular, the syntax and semantics of TWTL enable the compact representation of serial tasks, which are typically seen in robotics and control applications. This paper also discusses the relaxation of TWTL formulae with respect to deadlines of tasks. Efficient automata-based frameworks to solve synthesis, verification and learning problems are also presented. The key ingredient to the presented solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the specification. Case studies illustrating the expressivity of the logic and the proposed algorithms are included.

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